means the skill of handling people and delicate situations gracefully, saying or doing the right thing without giving offense

from From Latin tactus, 'a touching, a sense of touch,' from tangere, 'to touch' — the same root behind tangible, contact, and tangent. The literal sense of physical touch softened over time into a metaphorical one: the figurative 'delicate handling of others' arrived through French in the 18th century, the idea being that a tactful person has a fine, almost feeling sense for where the social tender spots lie.